FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Insphere Radius of Pentakis Dodecahedron given Midsphere Radius Formula

GoInsphere Radius of Pentakis Dodecahedron Formula

GoInsphere Radius of Pentakis Dodecahedron given Leg Length Formula

Fx Copy

LaTeX Copy

Insphere Radius of Pentakis Dodecahedron is the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere. Check FAQs

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{4 \cdot r m}{3 + \sqrt{5}})

r_i - Insphere Radius of Pentakis Dodecahedron?r_m - Midsphere Radius of Pentakis Dodecahedron?

Insphere Radius of Pentakis Dodecahedron given Midsphere Radius Example

With values

With units

Only example

Here is how the Insphere Radius of Pentakis Dodecahedron given Midsphere Radius equation looks like with Values.

Here is how the Insphere Radius of Pentakis Dodecahedron given Midsphere Radius equation looks like with Units.

Here is how the Insphere Radius of Pentakis Dodecahedron given Midsphere Radius equation looks like.

12.7326 = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{4 \cdot 13}{3 + \sqrt{5}})

12.7326m = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{4 \cdot 13m}{3 + \sqrt{5}})

12.7326 = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{4 \cdot 13}{3 + \sqrt{5}})

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Math » Category

Geometry » Category

3D Geometry » fx Insphere Radius of Pentakis Dodecahedron given Midsphere Radius

Insphere Radius of Pentakis Dodecahedron given Midsphere Radius Solution

Follow our step by step solution on how to calculate Insphere Radius of Pentakis Dodecahedron given Midsphere Radius?

FIRST Step Consider the formula

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{4 \cdot r m}{3 + \sqrt{5}})

Next Step Substitute values of Variables

∴

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{4 \cdot 13m}{3 + \sqrt{5}})

Next Step Prepare to Evaluate

∴

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{4 \cdot 13}{3 + \sqrt{5}})

Next Step Evaluate

∴

r i = 12.7326171113234m

LAST Step Rounding Answer

∴

r i = 12.7326m

Insphere Radius of Pentakis Dodecahedron given Midsphere Radius Formula Elements

Variables

Functions

Insphere Radius of Pentakis Dodecahedron

Insphere Radius of Pentakis Dodecahedron is the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Insphere Radius of Pentakis Dodecahedron

Midsphere Radius of Pentakis Dodecahedron

Midsphere Radius of Pentakis Dodecahedron is the radius of the sphere for which all the edges of the Pentakis Dodecahedron become a tangent line on that sphere.

Symbol: r_m

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Midsphere Radius of Pentakis Dodecahedron

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Insphere Radius of Pentakis Dodecahedron

Go Insphere Radius of Pentakis Dodecahedron

r i = \frac{(3 \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}})) \cdot l Base}{2}

Go Insphere Radius of Pentakis Dodecahedron given Leg Length

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{38 \cdot l Leg}{3 \cdot (9 + \sqrt{5})})

Go Insphere Radius of Pentakis Dodecahedron given Total Surface Area

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\sqrt{\frac{19 \cdot TSA}{15 \cdot (\sqrt{413 + (162 \cdot \sqrt{5})})}})

Go Insphere Radius of Pentakis Dodecahedron given Volume

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot ({(\frac{76 \cdot V}{15 \cdot (23 + (11 \cdot \sqrt{5}))})}^{\frac{1}{3}})

How to Evaluate Insphere Radius of Pentakis Dodecahedron given Midsphere Radius?

Insphere Radius of Pentakis Dodecahedron given Midsphere Radius evaluator uses Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5))) to evaluate the Insphere Radius of Pentakis Dodecahedron, Insphere Radius of Pentakis Dodecahedron given Midsphere Radius formula is defined as the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere, calculated using the midsphere radius of the Pentakis Dodecahedron. Insphere Radius of Pentakis Dodecahedron is denoted by r_i symbol.

How to evaluate Insphere Radius of Pentakis Dodecahedron given Midsphere Radius using this online evaluator? To use this online evaluator for Insphere Radius of Pentakis Dodecahedron given Midsphere Radius, enter Midsphere Radius of Pentakis Dodecahedron (r_m) and hit the calculate button.

FAQs on Insphere Radius of Pentakis Dodecahedron given Midsphere Radius

What is the formula to find Insphere Radius of Pentakis Dodecahedron given Midsphere Radius?

The formula of Insphere Radius of Pentakis Dodecahedron given Midsphere Radius is expressed as Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5))). Here is an example- 12.73262 = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((4*13)/(3+sqrt(5))).

How to calculate Insphere Radius of Pentakis Dodecahedron given Midsphere Radius?

With Midsphere Radius of Pentakis Dodecahedron (r_m) we can find Insphere Radius of Pentakis Dodecahedron given Midsphere Radius using the formula - Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Insphere Radius of Pentakis Dodecahedron?

Here are the different ways to Calculate Insphere Radius of Pentakis Dodecahedron-

Insphere Radius of Pentakis Dodecahedron=((3*(sqrt((81+(35*sqrt(5)))/218)))*Base Length of Pentakis Dodecahedron)/2
Insphere Radius of Pentakis Dodecahedron=(3/2)*(sqrt((81+(35*sqrt(5)))/218))*((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))
Insphere Radius of Pentakis Dodecahedron=(3/2)*(sqrt((81+(35*sqrt(5)))/218))*(sqrt((19*Total Surface Area of Pentakis Dodecahedron)/(15*(sqrt(413+(162*sqrt(5)))))))

Can the Insphere Radius of Pentakis Dodecahedron given Midsphere Radius be negative?

No, the Insphere Radius of Pentakis Dodecahedron given Midsphere Radius, measured in Length cannot be negative.

Which unit is used to measure Insphere Radius of Pentakis Dodecahedron given Midsphere Radius?

Insphere Radius of Pentakis Dodecahedron given Midsphere Radius is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Insphere Radius of Pentakis Dodecahedron given Midsphere Radius can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit